A novel technique is proposed for the simultaneous measurement of all three components of displacement from a single recording of the interference field in digital holographic interferometry. The interference field is divided into a number of rectangular segments, and in each of these segments, the interference field is represented as a multicomponent low-order two-dimensional (2D) polynomial phase signal. 2D-product high-order ambiguity function based analysis is applied to obtain an accurate estimation of the 2D polynomial coefficients. These coefficients are further used to compute the interference phases. The simulation and experimental results show the robustness of the proposed method to noise and its effectiveness in multiple phase estimation. (C) 2015 Optical Society of America